Debye-Huckel concept

The Debye-Huckel concept fails very soon (see Fig. 19) and probably earlier than in liquid electrolytes (at latest for 1 ). Also... 

As a result of these electrostatic effects aqueous solutions of electrolytes behave in a way that is non-ideal. This non-ideality has been accounted for successfully in dilute solutions by application of the Debye-Huckel theory, which introduces the concept of ionic activity. The Debye-Huckel Umiting law states that the mean ionic activity coefficient y+ can be related to the charges on the ions, and z, by the equation... 

This concept is due to Bjerrum, who in 1926 suggested that in simple electrolytes ions of the opposite charge could associate to form ion-pairs (Szwarc, 1965 Robinson Stokes, 1959). This concept of Bjerrum arose from problems with the Debye-Huckel theory, when the assumption that the electrostatic interaction was small compared with IcTwas not justified. 

The long-range term has been satisfactorily described by the Debye-Huckel formula and is retained. The short-range contribution is modeled by utilizing the concept of local compositions in a manner similar to Renon and Prausnitz (20) but with additional assumptions appropriate for electrolyte systems. Preliminary results suggest the validity of the model since good fits to experimental data have been obtained for a wide range of binary and ternary systems with only binary parameters. 

An important series of papers by Professor Pitzer and colleagues (26, 27, 28, 29), beginning in 1912, has laid the ground work for what appears to be the "most comprehensive and theoretically founded treatment to date. This treatment is based on the ion interaction model using the Debye-Huckel ion distribution and establishes the concept that the effect of short range forces, that is the second virial coefficient, should also depend on the ionic strength. Interaction parameters for a large number of electrolytes have been determined. 

Marshall s extensive review (16) concentrates mainly on conductance and solubility studies of simple (non-transition metal) electrolytes and the application of extended Debye-Huckel equations in describing the ionic strength dependence of equilibrium constants. The conductance studies covered conditions to 4 kbar and 800 C while the solubility studies were mostly at SVP up to 350 C. In the latter studies above 300°C deviations from Debye-Huckel behaviour were found. This is not surprising since the Debye-Huckel theory treats the solvent as incompressible and, as seen in Fig. 3, water rapidly becomes more compressible above 300 C. Until a theory which accounts for electrostriction in a compressible fluid becomes available, extrapolation to infinite dilution at temperatures much above 300 C must be considered untrustworthy. Since water becomes infinitely compressible at the critical point, the standard entropy of an ion becomes infinitely negative, so that the concept of a standard ionic free energy becomes meaningless. 

Following Debye-Huckel, the distribution of ions can be calculated via the Boltzmann energy distribution. The application of this law is based on the concept that the ion cloud represents a space charge which is most dense in the vicinity of the central ion and decreases with growing distance to the central ion. A number of simplifying assumptions concerning the state of ions is made ... 

The Debye-Hiickel theory discusses equilibrium properties of electrolyte solutions and allows the calculation of an activity coefficient for an individual ion, or equivalently, the mean activity coefficient of the electrolyte. Fundamental concepts of the Debye-Hiickel theory also form the basis of modern theories describing the non-equilibrium properties of electrolyte solutions such as diffusion and conductance. The Debye-Huckel theory is thus central to all theoretical approaches to electrolyte solutions. 

The ion-association concept relies on the use of Debye-Huckel based activity coefficients to calculate aqueous activities and is one that is employed most frequently in the models used today. A primary assumption of this approach is the use of the Macinnes convention such that for an aqueous solution containing equimolal concentrations of and Cl, their activities and hence activity coefficients are equivalent. This approach and convention were reexamined by Parkhurst in this volume, who explored the issue of mean salt based activity coefficients and the apparent... 

Thus the mobility must increase considerably to an extent dependent on the ratio of charge and radius. These considerations lead Me BaiN to attribute the fall of the conductivity to the formation of undissociated soap molecules, while Lotter-moSer thinks that neutral colloid is produced in these circumstances. This conception by Me Bain is very improbable according to Hartley, since the considerable increase of the solubility of the soap above the critical concentration is then inexplicable (see Fig. 3). Also it is not clear to what the considerable solvent power for organic compounds could be attributed. Everythii indicates that micelles are, in fact produced at the critical concentration. Such a micelle of many fatty acid anions may however be considered more or less as a polyvalent ion and this makes it probable that deviations from the classical laws of ions occur. In the first place large Debye-Huckel effects can be expected, while on the other hand, a large part of the counter ions will be bound. This latter must be found by a comparison of the conductivity and the transport numbers (Hartley ). From such an investigation it I... 

In the weak adsorption limit, we provide an exact analytical solution for polyelectrolyte-sphere adsorption by replacing the Debye-Huckel potential by the Hulthen potential. Other geometries require different approaches. As a generic concept, we propose application of the WKB method of quanmm mechanics, which we adopted to electrostatic polyelectrolyte adsorption problems. We have demonstrate that this description provides valuable analytical solutions and resolves a long-standing puzzle about the scaling properties of critical polyelectrolyte adsorption in curved geometries. 

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

The concept of pH and the ease with which it could be measured allowed the electrochemical ideas of Debye and Huckel to be applied to... 

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